This is a request for support of a Satellite Symposium on the mathematical modeling of circadian systems to be held on June 21, 1981 in conjunction with the Annual Meeting of the Association for the psychophysiological Study of Sleep (APSS): June 17-21, 1981. The meeting will be held at Dunfey's Hyannis Hotel on Cape Cod, Massachusetts. A meeting on the mathematical modeling of the circadian (approximately 24 hour) timing system is important to hold at this time. In the last few years, a large number of mathematical models have been developed but this activity has usually been isolated so that there is none of the normal interaction that should occur between those who have thought most about this problem. The proponents of the models belong to different scientific disciplines and normally never meet at national or international meetings. The proposed satellite synposium would bring together these investigators to ensure that the various proposed models are critically reviewed and their strengths and weaknesses in predicting periodic biological phenomena are fully understood. The APSS is particularly appropriate as a sponsor of this meeting because of the focus at their meetings on the circadian timing of the sleep-wake cycle and related biological rhythms and the relative sophistication of the audience. The papers of each participant and an edited transcription of the discussion will be published as a symposium volume. The published volume will serve as an important source for all those who are concerned about the temporal organization of human and animal behavior and physiology.